The layout of the maildirs is different in courier and dovecot, so you can not just switch between the two without manally adjusting the layot of each account.

The difference is that dovecot uses a "Maildir" directory, so you have to copy e.g. /var/vmail/domain.tld/user/Maildir/* to /var/vmail/domain.tld/user/

Additionally, in ispconfig, you have to change the imap server setings from dovecot to courier and from deliver to maildrop under System > server config > mail and then run the ispconfig updater on the shell and let it reconfigure services.